ICLR 2025 Papers

Procedural materials, represented as functional node graphs, are ubiquitous in computer graphics for photorealistic material appearance design. They allow users to perform intuitive and precise editing to achieve desired visual appearances. However, creating a procedural material given an input image requires professional knowledge and significant effort. In this work, we leverage the ability to convert procedural materials into standard Python programs and fine-tune a large pre-trained vision-language model (VLM) to generate such programs from input images. To enable effective fine-tuning, we also contribute an open-source procedural material dataset and propose to perform program-level augmentation by prompting another pre-trained large language model (LLM). Through extensive evaluation, we show that our method outperforms previous methods on both synthetic and real-world examples.

Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite their empirical observation, the theoretical understanding of these scaling laws remains limited. In this work, we employ techniques from statistical mechanics to analyze one-pass stochastic gradient descent within a student-teacher framework, where both the student and teacher are two-layer neural networks. Our study primarily focuses on the generalization error and its behavior in response to data covariance matrices that exhibit power-law spectra. For linear activation functions, we derive analytical expressions for the generalization error, exploring different learning regimes and identifying conditions under which power-law scaling emerges. Additionally, we extend our analysis to non-linear activation functions in the feature learning regime, investigating how power-law spectra in the data covariance matrix impact learning dynamics. Importantly, we find that the length of the symmetric plateau depends on the number of distinct eigenvalues of the data covariance matrix and the number of hidden units, demonstrating how these plateaus behave under various configurations. In addition, our results reveal a transition from exponential to power-law convergence in the specialized phase when the data covariance matrix possesses a power-law spectrum. This work contributes to the theoretical understanding of neural scaling laws and provides insights into optimizing learning performance in practical scenarios involving complex data structures.

Diffusion models excel in generative tasks, but aligning them with specific objectives while maintaining their versatility remains challenging. Existing fine-tuning methods often suffer from reward over-optimization, while approximate guidance approaches fail to optimize target rewards effectively. Addressing these limitations, we propose a training-free, test-time method based on Sequential Monte Carlo (SMC) to sample from the reward-aligned target distribution. Our approach, tailored for diffusion sampling and incorporating tempering techniques, achieves comparable or superior target rewards to fine-tuning methods while preserving diversity and cross-reward generalization. We demonstrate its effectiveness in single-reward optimization, multi-objective scenarios, and online black-box optimization. This work offers a robust solution for aligning diffusion models with diverse downstream objectives without compromising their general capabilities. Code is available at https://github.com/krafton-ai/DAS.

Diffusion models can effectively generate high-quality images. However, as they scale, rising memory demands and higher latency pose substantial deployment challenges. In this work, we aim to accelerate diffusion models by quantizing their weights and activations to 4 bits. At such an aggressive level, both weights and activations are highly sensitive, where existing post-training quantization methods like smoothing become insufficient. To overcome this limitation, we propose *SVDQuant*, a new 4-bit quantization paradigm. Different from smoothing, which redistributes outliers between weights and activations, our approach *absorbs* these outliers using a low-rank branch. We first consolidate the outliers by shifting them from activations to weights. Then, we use a high-precision, low-rank branch to take in the weight outliers with Singular Value Decomposition (SVD), while a low-bit quantized branch handles the residuals. This process eases the quantization on both sides. However, naively running the low-rank branch independently incurs significant overhead due to extra data movement of activations, negating the quantization speedup. To address this, we co-design an inference engine *Nunchaku* that fuses the kernels of the low-rank branch into those of the low-bit branch to cut off redundant memory access. It can also seamlessly support off-the-shelf low-rank adapters (LoRAs) without re-quantization. Extensive experiments on SDXL, PixArt-$\Sigma$, and FLUX.1 validate the effectiveness of SVDQuant in preserving image quality. We reduce the memory usage for the 12B FLUX.1 models by 3.5×, achieving 3.0× speedup over the 4-bit weight-only quantization (W4A16) baseline on the 16GB laptop 4090 GPU with INT4 precision. On the latest RTX 5090 desktop with Blackwell architecture, we achieve a 3.1× speedup compared to the W4A16 model using NVFP4 precision. Our quantization library and inference engine are available at https://github.com/mit-han-lab/deepcompressor/ and https://github.com/mit-han-lab/nunchaku/, correspondingly.

In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Every CPWL function has infinitely many such decompositions, but for applications in optimization and neural network theory, it is crucial to find decompositions with as few linear pieces as possible. This is a highly challenging problem, as we further demonstrate by disproving a recently proposed approach by Tran and Wang [Minimal representations of tropical rational functions. Algebraic Statistics, 15(1):27–59, 2024]. To make the problem more tractable, we propose to fix an underlying polyhedral complex determining the possible locus of nonlinearity. Under this assumption, we prove that the set of decompositions forms a polyhedron that arises as intersection of two translated cones. We prove that irreducible decompositions correspond to the bounded faces of this polyhedron and minimal solutions must be vertices. We then identify cases with a unique minimal decomposition, and illustrate how our insights have consequences in the theory of submodular functions. Finally, we improve upon previous constructions of neural networks for a given convex CPWL function and apply our framework to obtain results in the nonconvex case.

Model merging, such as model souping, is the practice of combining different models with the same architecture together without further training. In this work, we present a model merging methodology that addresses the difficulty of fine-tuning Large Language Models (LLMs) for target tasks in non-English languages, where task-specific data is often unavailable. We focus on mathematical reasoning and without in-language math data, facilitate cross-lingual transfer by composing language and math capabilities. Starting from the same pretrained model, we fine-tune separate "experts" on math instruction data in English and on generic instruction data in the target language. We then replace the top and bottom transformer layers of the math expert directly with layers from the language expert, which consequently enhances math performance in the target language. The resulting merged models outperform the individual experts and other merging methods on the math benchmark, MGSM, by 10% across four major languages where math instruction data is scarce. In addition, this layer swapping is simple, inexpensive, and intuitive, as it is based on an interpretative analysis of the most important parameter changes during the fine-tuning of each expert. The ability to successfully re-compose LLMs for cross-lingual transfer in this manner opens up future possibilities to combine model expertise, create modular solutions, and transfer reasoning capabilities across languages all post hoc.

Drug discovery is crucial for identifying candidate drugs for various diseases. However, its low success rate often results in a scarcity of annotations, posing a few-shot learning problem. Existing methods primarily focus on single-scale features, overlooking the hierarchical molecular structures that determine different molecular properties. To address these issues, we introduce Universal Matching Networks (UniMatch), a dual matching framework that integrates explicit hierarchical molecular matching with implicit task-level matching via meta- learning, bridging multi-level molecular representations and task-level generalization. Specifically, our approach explicitly captures structural features across multiple levels—atoms, substructures, and molecules—via hierarchical pooling and matching, facilitating precise molecular representation and comparison. Additionally, we employ a meta-learning strategy for implicit task-level matching, allowing the model to capture shared patterns across tasks and quickly adapt to new ones. This unified matching framework ensures effective molecular alignment while leveraging shared meta-knowledge for fast adaptation. Our experimental results demonstrate that UniMatch outperforms state-of-the-art methods on the MoleculeNet and FS-Mol benchmarks, achieving improvements of 2.87% in AUROC and 6.52% in ∆AUPRC. UniMatch also shows excellent generalization ability on the Meta-MolNet benchmark.

Generative models see increasing use in computer-aided drug design. However, while performing well at capturing distributions of molecular motifs, they often produce synthetically inaccessible molecules. To address this, we introduce SynFlowNet, a GFlowNet model whose action space uses chemical reactions and buyable reactants to sequentially build new molecules. By incorporating forward synthesis as an explicit constraint of the generative mechanism, we aim at bridging the gap between in silico molecular generation and real world synthesis capabilities. We evaluate our approach using synthetic accessibility scores and an independent retrosynthesis tool to assess the synthesizability of our compounds, and motivate the choice of GFlowNets through considerable improvement in sample diversity compared to baselines. Additionally, we identify challenges with reaction encodings that can complicate traversal of the MDP in the backward direction. To address this, we introduce various strategies for learning the GFlowNet backward policy and thus demonstrate how additional constraints can be integrated into the GFlowNet MDP framework. This approach enables our model to successfully identify synthesis pathways for previously unseen molecules.

It is commonly believed that, in a real-world environment, samples can only be drawn from observational and interventional distributions, corresponding to Layers 1 and 2 of the *Pearl Causal Hierarchy*. Layer 3, representing counterfactual distributions, is believed to be inaccessible by definition. However, Bareinboim, Forney, and Pearl (2015) introduced a procedure that allows an agent to sample directly from a counterfactual distribution, leaving open the question of what other counterfactual quantities can be estimated directly via physical experimentation. We resolve this by introducing a formal definition of realizability, the ability to draw samples from a distribution, and then developing a complete algorithm to determine whether an arbitrary counterfactual distribution is realizable given fundamental physical constraints, such as the inability to go back in time and subject the same unit to a different experimental condition. We illustrate the implications of this new framework for counterfactual data collection using motivating examples from causal fairness and causal reinforcement learning. While the baseline approach in these motivating settings typically follows an interventional or observational strategy, we show that a counterfactual strategy provably dominates both.

The *missing mass* refers to the proportion of data points in an *unknown* population of classifier inputs that belong to classes *not* present in the classifier's training data, which is assumed to be a random sample from that unknown population. We find that *in expectation* the missing mass is entirely determined by the number $f_k$ of classes that *do* appear in the training data the same number of times *and an exponentially decaying error*. While this is the first precise characterization of the expected missing mass in terms of the sample, the induced estimator suffers from an impractically high variance. However, our theory suggests a large search space of nearly unbiased estimators that can be searched effectively and efficiently. Hence, we cast distribution-free estimation as an optimization problem to find a distribution-specific estimator with a minimized mean-squared error (MSE), given only the sample. In our experiments, our search algorithm discovers estimators that have a substantially smaller MSE than the state-of-the-art Good-Turing estimator. This holds for over 93\% of runs when there are at least as many samples as classes. Our estimators' MSE is roughly 80\% of the Good-Turing estimator's.

Text watermarking for Large Language Models (LLMs) has made significant progress in detecting LLM outputs and preventing misuse. Current watermarking techniques offer high detectability, minimal impact on text quality, and robustness to text editing. However, current researches lack investigation into the imperceptibility of watermarking techniques in LLM services. This is crucial as LLM providers may not want to disclose the presence of watermarks in real-world scenarios, as it could reduce user willingness to use the service and make watermarks more vulnerable to attacks. This work is the first to investigate the imperceptibility of watermarked LLMs. We design an identification algorithm called Water-Probe that detects watermarks through well-designed prompts to the LLM. Our key motivation is that current watermarked LLMs expose consistent biases under the same watermark key, resulting in similar differences across prompts under different watermark keys. Experiments show that almost all mainstream watermarking algorithms are easily identified with our well-designed prompts, while Water-Probe demonstrates a minimal false positive rate for non-watermarked LLMs. Finally, we propose that the key to enhancing the imperceptibility of watermarked LLMs is to increase the randomness of watermark key selection. Based on this, we introduce the Water-Bag strategy, which significantly improves watermark imperceptibility by merging multiple watermark keys.

Deep graph learning has gained grand popularity over the past years due to its versatility and success in representing graph data across a wide range of domains. However, the pervasive issue of imbalanced graph data distributions, where certain parts exhibit disproportionally abundant data while others remain sparse, undermines the efficacy of conventional graph learning algorithms, leading to biased outcomes. To address this challenge, Imbalanced Graph Learning (IGL) has garnered substantial attention, enabling more balanced data distributions and better task performance. Despite the proliferation of IGL algorithms, the absence of consistent experimental protocols and fair performance comparisons pose a significant barrier to comprehending advancements in this field. To bridge this gap, we introduce **IGL-Bench**, a foundational comprehensive benchmark for imbalanced graph learning, embarking on **17** diverse graph datasets and **24** distinct IGL algorithms with uniform data processing and splitting strategies. Specifically, IGL-Bench systematically investigates state-of-the-art IGL algorithms in terms of **effectiveness**, **robustness**, and **efficiency** on node-level and graph-level tasks, with the scope of class-imbalance and topology-imbalance. Extensive experiments demonstrate the potential benefits of IGL algorithms on various imbalanced conditions, offering insights and opportunities in the IGL field. Further, we have developed an open-sourced and unified package to facilitate reproducible evaluation and inspire further innovative research, available at: https://github.com/RingBDStack/IGL-Bench.

In typical multimodal contrastive learning, such as CLIP, encoders produce one point in the latent representation space for each input. However, one-point representation has difficulty in capturing the relationship and the similarity structure of a huge amount of instances in the real world. For richer classes of the similarity, we propose the use of weighted point sets, namely, sets of pairs of weight and vector, as representations of instances. In this work, we theoretically show the benefit of our proposed method through a new understanding of the contrastive loss of CLIP, which we call symmetric InfoNCE. We clarify that the optimal similarity that minimizes symmetric InfoNCE is the pointwise mutual information, and show an upper bound of excess risk on downstream classification tasks of representations that achieve the optimal similarity. In addition, we show that our proposed similarity based on weighted point sets consistently achieves the optimal similarity. To verify the effectiveness of our proposed method, we demonstrate pretraining of text-image representation models and classification tasks on common benchmarks.

To confirm that the expressive power of ReLU neural networks grows with their depth, the function $F_n = \max (0,x_1,\ldots,x_n )$ has been considered in the literature. A conjecture by Hertrich, Basu, Di Summa, and Skutella [NeurIPS 2021] states that any ReLU network that exactly represents $F_n$ has at least $\lceil \log_2 (n+1) \rceil$ hidden layers. The conjecture has recently been confirmed for networks with integer weights by Haase, Hertrich, and Loho [ICLR 2023]. We follow up on this line of research and show that, within ReLU networks whose weights are decimal fractions, $F_n$ can only be represented by networks with at least $\lceil \log_3 (n+1) \rceil$ hidden layers. Moreover, if all weights are $N$-ary fractions, then $F_n$ can only be represented by networks with at least $\Omega( \frac{\ln n}{\ln \ln N})$ layers. These results are a partial confirmation of the above conjecture for rational ReLU networks, and provide the first non-constant lower bound on the depth of practically relevant ReLU networks.

Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is frequently limited by the substantial computational resources required to construct the Kohn-Sham Hamiltonian. In response to these limitations, current research has employed deep-learning models to efficiently predict molecular and solid Hamiltonians, with roto-translational symmetries encoded in their neural networks. However, the scalability of prior models may be problematic when applied to large molecules, resulting in non-physical predictions of ground-state properties. In this study, we generate a substantially larger training set (PubChemQH) than used previously and use it to create a scalable model for DFT calculations with physical accuracy. For our model, we introduce a loss function derived from physical principles, which we call Wavefunction Alignment Loss (WALoss). WALoss involves performing a basis change on the predicted Hamiltonian to align it with the observed one; thus, the resulting differences can serve as a surrogate for orbital energy differences, allowing models to make better predictions for molecular orbitals and total energies than previously possible. WALoss also substantially accelerates self-consistent-field (SCF) DFT calculations. Here, we show it achieves a reduction in total energy prediction error by a factor of 1347 and an SCF calculation speed-up by a factor of 18\%. These substantial improvements set new benchmarks for achieving accurate and applicable predictions in larger molecular systems.

In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while reducing computational costs by deriving descent directions in randomly selected low-dimensional subspaces. This paper proposes the Random Subspace Homogenized Trust Region (RSHTR) method with the best theoretical guarantees among random subspace algorithms for nonconvex optimization. RSHTR achieves an $\varepsilon$-approximate first-order stationary point in $O(\varepsilon^{-3/2})$ iterations, converging locally at a linear rate. Furthermore, under rank-deficient conditions, RSHTR satisfies $\varepsilon$-approximate second-order necessary conditions in $O(\varepsilon^{-3/2})$ iterations and exhibits a local quadratic convergence. Experiments on real-world datasets verify the benefits of RSHTR.

Nowadays, temporal heterogeneous graphs attract much research and industrial attention for building the next-generation Relational Deep Learning models and applications, due to their informative structures and features. While providing timely and precise services like personalized recommendations and question answering, this rich information also introduces extra exposure risk for each node in the graph. The distinctive local topology, the abundant heterogeneous features, and the time dimension of the graph data are more prone to expose sensitive information and narrow down the scope of victim candidates, which calls for well-defined protection techniques on graphs. To this end, we propose a Temporal Heterogeneous Graph Generator balancing Privacy, Utility, and Efficiency, named THePUff. More specifically, we first propose a differential privacy algorithm to perturb the input temporal heterogeneous graph for protecting privacy, and then utilize both the perturbed graph and the original one in a generative adversarial setting for THePUff to learn and generate privacy-guaranteed and utility-preserved graph data in an efficient manner. We further propose 6 new metrics in the temporal setting to measure heterogeneous graph utility and privacy. Finally, based on temporal heterogeneous graph datasets with up to 1 million nodes and 20 million edges, the experiments show that THePUff generates utilizable temporal heterogeneous graphs with privacy protected, compared with state-of-the-art baselines.

Large language models (LLMs) store extensive factual knowledge, but the mechanisms behind how they store and express this knowledge remain unclear. The Knowledge Neuron (KN) thesis is a prominent theory for explaining these mechanisms. This theory is based on the **Knowledge Localization (KL)** assumption, which suggests that a fact can be localized to a few knowledge storage units, namely knowledge neurons. However, this assumption has two limitations: first, it may be too rigid regarding knowledge storage, and second, it neglects the role of the attention module in knowledge expression. In this paper, we first re-examine the KL assumption and demonstrate that its limitations do indeed exist. To address these, we then present two new findings, each targeting one of the limitations: one focusing on knowledge storage and the other on knowledge expression. We summarize these findings as **Query Localization** assumption and argue that the KL assumption can be viewed as a simplification of the QL assumption. Based on QL assumption, we further propose the Consistency-Aware KN modification method, which improves the performance of knowledge modification, further validating our new assumption. We conduct 39 sets of experiments, along with additional visualization experiments, to rigorously confirm our conclusions. Code will be made public soon.

One of the most practical and challenging types of black-box adversarial attacks is the hard-label attack, where only the top-1 predicted label is available. One effective approach is to search for the optimal ray direction from the benign image that minimizes the $\ell_p$ norm distance to the adversarial region. The unique advantage of this approach is that it transforms the hard-label attack into a continuous optimization problem. The objective function value is the ray's radius, which can be obtained via binary search at a high query cost. Existing methods use a "sign trick" in gradient estimation to reduce the number of queries. In this paper, we theoretically analyze the quality of this gradient estimation and propose a novel prior-guided approach to improve ray search efficiency both theoretically and empirically. Specifically, we utilize the transfer-based priors from surrogate models, and our gradient estimators appropriately integrate them by approximating the projection of the true gradient onto the subspace spanned by these priors and random directions, in a query-efficient manner. We theoretically derive the expected cosine similarities between the obtained gradient estimators and the true gradient, and demonstrate the improvement achieved by incorporating priors. Extensive experiments on the ImageNet and CIFAR-10 datasets show that our approach significantly outperforms 11 state-of-the-art methods in terms of query efficiency.